In triangle XYZ ,  <X =42°, < Y =78°, < z=60° name the longest side, the shortest side.

In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Given triangle \( XYZ \), we have the following angles:
- \( \angle X = 42^\circ \)
- \( \angle Y = 78^\circ \)
- \( \angle Z = 60^\circ \)

### Identifying the Longest Side
- The largest angle is \( \angle Y = 78^\circ \).
- Therefore, the longest side is opposite this angle, which is side \( XZ \).

### Identifying the Shortest Side
- The smallest angle is \( \angle X = 42^\circ \).
- Therefore, the shortest side is opposite this angle, which is side \( YZ \).

### Conclusion:
- The **longest side** is \( XZ \).
- The **shortest side** is \( YZ \).

Would you like more details on this concept or have any other questions?

Here are some related questions you might find interesting:
1. How do you calculate the side lengths of a triangle using the Sine Rule?
2. How would the sides compare if the triangle was a right triangle?
3. What is the relationship between angles and side lengths in an equilateral triangle?
4. How can you determine if a triangle is scalene, isosceles, or equilateral just by looking at the angles?
5. Can you calculate the area of triangle \( XYZ \) if you know one side length?

**Tip:** In any triangle, the side lengths are directly proportional to the sine of their opposite angles.

Understand how to identify the longest and shortest sides in triangle XYZ based on given angle measurements (42°, 78°, 60°). Explore the relationship between angles and side lengths in triangles with a detailed explanation and examples.

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